Placeholder Image

Subtitles section Play video

  • - We're not going to do a few examples questions

  • from the Khan academy exercise

  • on the standard algorithms.

  • We're asked, which of the following

  • correctly multiplies 74 times 8

  • using the standard algorithm.

  • So pause this video and see if you can work on that

  • before we do it together.

  • All right, now let's just remind ourselves

  • what the standard algorithm is.

  • In fact, let's just remind ourselves what an algorithm is.

  • An algorithm is a series of steps that you can do

  • to do something, so you'll often hear about

  • a computer algorithm.

  • But you can also have algorithms in math,

  • just a method for doing something.

  • And the standard algorithm,

  • that's the typical, or the standard, way

  • that a lot of people will tackle

  • a multiplication question or computation like this.

  • But just as a reminder, in the standard algorithm

  • if we're multiplying 74 times 8

  • we would write the eight in the ones place

  • right below the four in the ones place,

  • and then you multiply each of these places times the eight.

  • So you would start with the four times the eight,

  • you would get 32.

  • 32 you can express as two ones and three tens.

  • So we'll put that three up there.

  • And then you would multiple the seven times the eight.

  • Seven times eight is 56, and that's going to be 56 tens

  • because it's seven 10s times eight is 56 tens.

  • Plus the three 10s you had before

  • get you to 59 tens, and so you would write over here.

  • That's 59 tens, and so this would be 592.

  • Now when you look at the choices,

  • that's exactly what happened here in choice C.

  • Just for kicks we can see what went wrong

  • in these other ones.

  • Let's see, in this first one,

  • when we multiplied the,

  • when we multiplied the four ones times eight ones,

  • according to this, this person somehow got

  • three ones and two tens, and 23.

  • Four times eight is not 23, you can rule that one out.

  • And here when they multiplied

  • the four ones times the eight ones,

  • that would be the 32.

  • So it's two ones and then another three tens,

  • so there should've been a three up here.

  • And so that way when you multiplied

  • the seven tens times eight,

  • you get 56 but then you add this other three tens

  • so you would really need to get to 59 tens.

  • So that's why that one didn't work.

  • Let's do another example here.

  • And this is going to be with a different type of question.

  • So here we are told that,

  • Don starts to use the standard algorithm

  • to solve 418 times five.

  • His work is shown below.

  • What number should Don replace Y with?

  • Pause this video and see if you can figure it out.

  • Okay, so the way to think about this,

  • this might at first confuse you a little bit,

  • because Y, and why is there a Y there, in the first place?

  • But what they're really trying to get at

  • is making sure that you, or we, understand

  • what Don is trying to do when

  • he's trying to do the standard algorithms.

  • So as we just highlighted in last example,

  • the way that we would tackle this

  • with the standard algorithm,

  • and actually let me write it down, 418 times five.

  • We would say eight ones times five ones

  • is going to be 40 ones.

  • 40 ones we can write as zero ones and four tens.

  • And so that looks like the place where they,

  • where Don stopped computing.

  • So he's on his way to solving the whole thing

  • he just partially computed it so far.

  • But just by doing that, we know what the Y should be.

  • The Y should be four.

  • So what number should Don replace the Y with?

  • He should replace it with a four,

  • and it's representing Y tens, or four tens.

  • And of course you could keep going with this computation.

  • If Don were to say, okay, I have one ten times five,

  • that'd be five tens, plus another four tens,

  • that's nine tens.

  • And then last but not least,

  • if Don wanted to figure out, well,

  • he's got four hundreds here times five

  • is twenty hundreds,

  • which we can express as zero hundreds and two thousands.

  • Or you just do this as 20 hundreds.

  • So they're not asking us to do the entire computation.

  • We're just trying to figure out

  • what Don did essentially in this first step.

  • What number should he have written here instead of a Y?

  • So Y could be replaced with a four.

  • It's representing the four,

  • which is really in the tens place, so four tens.

- We're not going to do a few examples questions

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

A2 algorithm standard multiplied computation replace place

Worked examples for standard algorithm exercise

  • 2 0
    林宜悉 posted on 2020/03/27
Video vocabulary